A journal of IEEE and CAA , publishes high-quality papers in English on original theoretical/experimental research and development in all areas of automation
Volume 7 Issue 3
Apr.  2020

IEEE/CAA Journal of Automatica Sinica

  • JCR Impact Factor: 11.8, Top 4% (SCI Q1)
    CiteScore: 17.6, Top 3% (Q1)
    Google Scholar h5-index: 77, TOP 5
Turn off MathJax
Article Contents
Qinqin Zhu, "Latent Variable Regression for Supervised Modeling and Monitoring," IEEE/CAA J. Autom. Sinica, vol. 7, no. 3, pp. 800-811, May 2020. doi: 10.1109/JAS.2020.1003153
Citation: Qinqin Zhu, "Latent Variable Regression for Supervised Modeling and Monitoring," IEEE/CAA J. Autom. Sinica, vol. 7, no. 3, pp. 800-811, May 2020. doi: 10.1109/JAS.2020.1003153

Latent Variable Regression for Supervised Modeling and Monitoring

doi: 10.1109/JAS.2020.1003153
Funds:  This work was supported by the Chemical Engineering Department at the University of Waterloo
More Information
  • A latent variable regression algorithm with a regularization term (rLVR) is proposed in this paper to extract latent relations between process data X and quality data Y . In rLVR, the prediction error between X and Y is minimized, which is proved to be equivalent to maximizing the projection of quality variables in the latent space. The geometric properties and model relations of rLVR are analyzed, and the geometric and theoretical relations among rLVR, partial least squares, and canonical correlation analysis are also presented. The rLVR-based monitoring framework is developed to monitor process-relevant and quality-relevant variations simultaneously. The prediction and monitoring effectiveness of rLVR algorithm is demonstrated through both numerical simulations and the Tennessee Eastman (TE) process.


  • loading
  • 1$ \gamma = \kappa\lambda_w $, where $ \lambda_w $ is the Lagrange multiplier for $ {{w}} $.
  • [1]
    J. F. MacGregor, C. Jaeckle, C. Kiparissides, and M. Koutoudi, “Process monitoring and diagnosis by multiblock PLS methods,” AIChE Journal, vol. 40, no. 5, pp. 826–838, 1994. doi: 10.1002/aic.690400509
    S. Joe Qin, “Statistical process monitoring: basics and beyond,” J. Chemometrics, vol. 17, no. 8–9, pp. 480–502, 2003. doi: 10.1002/cem.800
    X. Zhang, W. W. Yan, X. Zhao, and H. H. Shao, “Nonlinear biological batch process monitoring and fault identification based on kernel fisher discriminant analysis,” Process Biochemistry, vol. 42, no. 8, pp. 1200–1210, Aug. 2007. doi: 10.1016/j.procbio.2007.05.016
    A. P. Ferreira and M. Tobyn, “Multivariate analysis in the pharmaceutical industry: enabling process understanding and improvement in the PAT and QbD era,” Pharmaceutical Development and Technology, vol. 20, no. 5, pp. 513–527, 2015. doi: 10.3109/10837450.2014.898656
    X. Luo, M. C. Zhou, Y. N. Xia, Q. S. Zhu, A. C. Ammari, and A. Alabdulwahab, “Generating highly accurate predictions for missing QoS data via aggregating nonnegative latent factor models,” IEEE Trans. Neural Networks and Learning Systems, vol. 27, no. 3, pp. 524–537, Apr. 2015.
    X. Luo, M. C. Zhou, S. Li, Y. N. Xia, Z.-H. You, Q. S. Zhu, and H. Leung, “Incorporation of efficient second-order solvers into latent factor models for accurate prediction of missing QoS data,” IEEE Trans. Cybernetics, vol. 48, no. 4, pp. 1216–1228, Apr. 2017.
    J. E. Jackson, A User’s Guide to Principal Components. John Wiley & Sons, 2005, vol. 587.
    S. J. Qin, “Survey on data-driven industrial process monitoring and diagnosis,” Annual Reviews in Control, vol. 36, no. 2, pp. 220–234, 2012. doi: 10.1016/j.arcontrol.2012.09.004
    D. H. Zhou, G. Li, and S. J. Qin, “Total projection to latent structures for process monitoring,” AIChE Journal, vol. 56, no. 1, pp. 168–178, Jan. 2019.
    S. J. Qin and Y. Y. Zheng, “Quality-relevant and process-relevant fault monitoring with concurrent projection to latent structures,” AIChE Journal, vol. 59, no. 2, pp. 496–504, Feb. 2013. doi: 10.1002/aic.13959
    L. Sun, S. W. Ji, S. P. Yu, and J. P. Ye, “On the equivalence between canonical correlation analysis and orthonormalized partial least squares,” in Proc. 21st Int. Joint Conf. Artificial Intelligence, vol. 9, pp. 1230–1235, 2009.
    Q. Q. Zhu, Q. Liu, and S. J. Qin, “Concurrent quality and process monitoring with canonical correlation analysis,” J. Process Control, vol. 60, pp. 95–103, Dec. 2017. doi: 10.1016/j.jprocont.2017.06.017
    G. Li, S. J. Qin, and D. H. Zhou, “Geometric properties of partial least squares for process monitoring,” Automatica, vol. 46, no. 1, pp. 204–210, Jan. 2010. doi: 10.1016/j.automatica.2009.10.030
    Z. W. Chen, S. X. Ding, K. Zhang, Z. B. Li, and Z. K. Hu, “Canonical correlation analysis-based fault detection methods with application to alumina evaporation process,” Control Engineering Practice, vol. 46, pp. 51–58, Jan. 2016. doi: 10.1016/j.conengprac.2015.10.006
    Q. Zhu and S. J. Qin, “Supervised diagnosis of quality and process faults with canonical correlation analysis,” Industrial & Engineering Chemistry Research, 2019.
    Q. C. Jiang, X. F. Yan, and B. Huang, “Neighborhood variational bayesian multivariate analysis for distributed process monitoring with missing data,” IEEE Trans. Control Systems Technology, vol. 27, no. 6, pp. 2330–2339, Oct. 2018.
    Q. C. Jiang, X. F. Yan, and B. Huang, “Review and perspectives of data-driven distributed monitoring for industrial plant-wide processes,” Industrial &Engineering Chemistry Research, vol. 58, no. 29, pp. 12899–12912, 2019.
    Z. Q. Ge, “Distributed predictive modeling framework for prediction and diagnosis of key performance index in plant-wide processes,” J. Process Control, vol. 65, pp. 107–117, May 2018. doi: 10.1016/j.jprocont.2017.08.010
    P. Geladi and B. R. Kowalski, “Partial least-squares regression: a tutorial,” Analytica Chimica Acta, vol. 185, pp. 1–17, 1986. doi: 10.1016/0003-2670(86)80028-9
    A. Höskuldsson, “PLS regression methods,” J. Chemometrics, vol. 2, no. 3, pp. 211–228, 1988. doi: 10.1002/cem.1180020306
    H. Hotelling, “Relations between two sets of variates,” Biometrika, vol. 28, no. 3/4, pp. 321–377, 1936. doi: 10.2307/2333955
    Q. Q. Zhu and S. J. Qin, “Latent variable regression for process and quality modeling, ” in 1st Int. Conf. on Industrial Artificial Intelligence (IAI). IEEE, 2019, pp. 1–6.
    Q. Q. Zhu, S. J. Qin, and Y. Dong, “Dynamic latent variable regression for inferential sensor modeling and supervised monitoring,” Submitted to Computers &Chemical Engineering, 2019.
    Q. Q. Zhu, “Dynamic latent variable regression for inferential sensor modeling and supervised monitoring,” Submitted to 21st IFAC World Congress, 2019.
    R. Rosipal and N. Krämer, “Overview and recent advances in partial least squares,” in Proc. Int. Statistical and Optimization Perspectives Workshop “Subspace, Latent Structure and Feature Selection,” Berlin, Germany: Springer, 2005, pp. 34–51.
    J. J. Downs and E. F. Vogel, “A plant-wide industrial process control problem,” Computers &Chemical Engineering, vol. 17, no. 3, pp. 245–255, 1993.


    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Figures(16)  / Tables(4)

    Article Metrics

    Article views (1193) PDF downloads(60) Cited by()


    DownLoad:  Full-Size Img  PowerPoint